The equation y = k / (x^2) expresses that y and x are inversely proportional with k as the constant of proportionality. As x increases, y decreases, reflecting an inverse square relationship.
The mathematical representation for the verbal statement "y varies inversely as the square of x" is:
y = k / (x^2)
In this equation:
y is the dependent variable.
x is the independent variable.
k is the constant of proportionality.
This equation signifies that as x increases, y decreases, and vice versa. The relationship between y and x is inversely proportional, with the square of x in the denominator, indicating the inverse square relationship.
In this mathematical model, the inverse square relationship implies that the effect of changes in x on y is amplified due to the squared term, reinforcing the strong inverse correlation between the two variables.